Cartography involves creating maps to accurately convey spatial information about physical reality. Map-making has a long history, dating back to a wall painting from Çatalhöyük, dating to the late 7th millennium BCE. The ancient Greeks and Romans created maps as early as the 6th century BCE, and Ptolemy’s 2nd-century CE treatise, Geographia, included his world map.
A close connection exists between cartography and perspective. Ptolemy’s planisphere, which imagines the eye at the south pole and projects key celestial lines onto the equator. This method employs the three basic elements of linear perspective: a fixed eye point, a picture plane, and a spatial object.
Terrestrial Map Making
A projection transforms the curved surface of the globe into a flat plane, requiring the conversion of locations into coordinates. All projections distort the surface in some way; common types include stereographic, Lambert, and Mercator.
Coordinates are typically given as latitude and longitude. Map projection goes beyond perspective projections like shadow casting or pinhole camera images; it includes any mathematical function that transforms curved coordinates onto a flat plane. Thus, few practical projections are actually perspective projections. Yet, cartographic perspective projections are among the first applications of linear perspective elements (object, eye-point, surface).
Terrestrial Globe
A terrestrial globe is a spherical model of Earth or another celestial body that accurately represents its surface without distortion, except for scale. It serves similar purposes to terrestrial maps and enables various analyses of visual perception. The globe displays landmasses, bodies of water, nations, cities, and latitude and longitude lines. Some have dimensional relief for mountains.
Innovations in Map Making
We have already established the close links between the principles of perspective and geometry, optics, surveying, sundials, and astronomy. However, cartography and map-making likewise have close connections to the development of both linear and parallel perspective, plus related sub-types.
Ptolemy created a regular planisphere that imagines the eye at the south pole, uses the equator as the picture plane, and projects onto it the tropics of Cancer and Capricorn, plus the ecliptic. Over the subsequent centuries, the problem of transforming spherical earth coordinates into a flat map became central to cartography and navigation. The systematic study of these possibilities began in the sixteenth century, when the rectilinear projection plane was shifted to a position at right angles to the equator, which led to further developments in cartography. The position of the (sometimes imaginary) candle / illuminating point varied.
Projections of a 3-D sphere onto a flat surface distort the sphere; and various types of projection are employed, including stereographic, Lambert, and Mercator. The 2-D Mercator projection is a conformal cylindrical map projection first presented by Flemish mapmaker Gerardus Mercator in 1569, and it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines. Rhumb lines are lines of direction that cross meridians at a constant angle, and meridians of longitude and parallels of latitude are special cases of rhumb lines, whereby in a map projection, coordinates are normally expressed as latitude and longitude.
Google Earth is a New Media application that provides a 3-D view of Earth and is used for exploration. It lets a person look around and see what things are like from different points of view, using a combination of satellite views, 3-D renderings, 3-D modelling, plus texture mapping, etc. You can get a useful feel for the geometry of a scene, including the size of buildings and the 3-D topography of areas.
Google Maps is a New Media application that lets users view a 2-D projection of regions of the Earth. It can be used for local GPS tracing, traffic detection, and transport information. Google Maps offers satellite imagery, aerial photography, and street maps, enabling route planning for walking, driving, biking, and flying. Google Maps’ satellite view is a “top-down” or bird’s-eye perspective. Notably, recent versions ditched the 2-D Mercator projection in favour of a zoomable 3-D globe projection.
Next, we explore the Gott Projection, the first new map in a century!
Gott Projection
Many kinds of mapping projections are known, but none have been developed in quite some time. Then, recently in 2021, Dr. J. Richard Gott invented a new Azimuthal projection, a double-sided disk map designed to minimise all types of map distortions. Gott reimagined maps of the earth, in which not only the sizes of landmasses change but also their shapes and distances from one another.
Dr. Gott wanted to strike a balance between the three kinds of errors: size, shape, and distance, and he worked out a scoring system that could sum these different kinds of errors. He then examined all possible projections and found the one that minimised the sum of the three kinds of error, which turned out to be the Winkel-Tripel projection. However, a distortion persisted, being a mathematical incision line or breakpoint, often running from pole to pole down the Pacific.
The resulting shape cannot be stretched and pulled back over the unbroken surface of a sphere. A solution was found in a new kind of double-sided map that skips the oddly shaped topological boundary entirely. The resulting circular map simply wraps around the edge. It is not a true map because you can see only half of the planet at once; but this is no different from the 3-D globe, because in the double-sided map, you simply flip it.
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